Spectral Instability Research Articles

Dynamical and variational properties of the NLS-[formula omitted] equation on the star graph

We study the nonlinear Schrödinger equation with δs′ coupling of intensity β∈R∖{0} on the star graph Γ consisting of N half-lines. The nonlinearity has the form g(u)=|u|p−1u,p>1. In the first part of the paper, under certain restriction on β, we prove the existence of the ground state solution as a minimizer of the action functional Sω on the Nehari manifold. It appears that the family of critical points which contains a ground state consists of N profiles (one symmetric and N−1 asymmetric). In particular, for the attractive δs′ coupling (β<0) and the frequency ω above a certain threshold, we managed to specify the ground state.The second part is devoted to the study of orbital instability of the critical points. We prove spectral instability of the critical points using Grillakis/Jones Instability Theorem. Then orbital instability for p>2 follows from the fact that data-solution mapping associated with the equation is of class C2 in H1(Γ). Moreover, for p>5 we complete and concertize instability results showing strong instability (by blow up in finite time) for the particular critical points.

Spectral Stable Blue-Light-Emitting Diodes via Asymmetric Organic Diamine Based Dion-Jacobson Perovskites.

The spectral instability issue is a challenge in blue perovskite light-emitting diodes (PeLEDs). Dion–Jacobson (DJ) phase perovskites are promising alternatives to achieve high-quality blue PeLEDs. However, the current exploration of DJ phase perovskites is focused on symmetric divalent cations, and the corresponding efficiency of blue PeLEDs is still inferior to that of green and red ones. In this work, we report a new type of DJ phase CsPb(Br/Cl)3 perovskite via introduction of an asymmetric molecular configuration as the organic spacer cation in perovskites. The primary and tertiary ammonium groups on the asymmetric cations bridge with the lead halide octahedra forming the DJ phase structures. Stable photoluminescence spectra were demonstrated in perovskite films owing to the suppressed halide segregation. Meanwhile, the radiative recombination efficiency of charges is improved significantly as a result of the confinement effects and passivation of charge traps. Finally, we achieved an external quantum efficiency of 2.65% in blue PeLEDs with stable spectra emission under applied bias voltages. To our best knowledge, this is the first report of asymmetric cations used in PeLEDs, which provides a facile solution to the halide segregation issue in PeLEDs.

Pseudospectrum of Reissner-Nordström black holes: Quasinormal mode instability and universality

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, so it is critical to understand if the quasinormal mode spectrum is stable against perturbations. It was recently shown that the pseudospectrum can shed light on the spectral stability of black hole quasinormal modes. We study the pseudospectrum of Reissner-Nordstr\"om spacetimes and we find a spectral instability of scalar and gravitoelectric quasinormal modes in subextremal and extremal black holes, extending similar findings for the Schwarzschild spacetime. The asymptotic structure of pseudospectral contour levels is the same for scalar and gravitoelectric perturbations. By making different gauge choices in the hyperboloidal slicing of the spacetime, we find that the broad features of the pseudospectra are remarkably gauge-independent. The gravitational-led and electromagnetic-led quasinormal modes of extremal Reissner-Nordstr\"om black holes exhibit "strong" isospectrality: not only their spectrum coincides, but the whole pseudospectrum is the same for both classes of perturbations. We observe that a conformal duality between the extremal horizon and spacetime boundaries at infinity is responsible for such "strong" isospectrality property.

Nonlinear dynamics of fluid-conveying composite pipes subjected to time-varying axial tension in sub- and super-critical regimes

In the present work, nonlinear dynamics of a simply-supported fluid-conveying composite pipe subjected to axial tension in sub- and super-critical regimes are investigated. The tension acting on the pipe is assumed to comprise an average component and a harmonically changing disturbance component. More specifically, the nonlinear equation of motion is derived based on the Euler-Bernoulli beam theory considering the von Kármán nonlinearity for large deformation assumption, which is then truncated via the Galerkin's approach. In addition, the Kelvin-Voigt model is adopted on the pipe materials with visco-elastic structural damping. Afterwards, parametric studies are performed to evaluate the effects of the axial tension and fiber orientation angle on pre- and post-buckling frequencies, critical fluid velocities and static buckling displacements. The global dynamic behaviors of the pipe are studied through the forms of bifurcation diagrams, phase portraits, Poincaré maps, power spectral density (PSD) diagrams and linear instability maps, in both sub- and super-critical regimes. The results show that, based on symmetric layers, pipes with smaller fiber orientation angles have larger critical divergence fluid velocities but smaller static buckling displacements. Some interesting dynamical phenomena, including periodic, multi-periodic, quasi-periodic and chaotic motions, can be observed with different fiber orientation angles. Moreover, the system shows ‘soft spring’ characteristic in super-critical regime, compared with the ‘hard spring’ characteristic in sub-critical case.

ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

AbstractThe purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.

Mixed Halide Perovskite Films by Vapor Anion Exchange for Spectrally Stable Blue Stimulated Emission.

Solution-processed all-inorganic CsPbX3 perovskites exhibit outstanding optoelectronic properties and are being considered as a promising optical gain medium, with impressive performance in the green and red region. However, the development of CsPbX3 for blue emission is still lagging far behind, owing to difficulties in thin films synthesis and spectral instability subject to light irradiation. Here, a facile vapor anion exchange (VAE) method that enables preparation of blue-emitting perovskite films with both excellent surface morphology and good photo-stability is reported. The mixed-Br/Cl quasi-2D perovskite films show spectrally stable pure blue emission (471nm) under continuous-wave laser irradiation with power density as high as 81Wcm-2 . Furthermore, optically pumped blue amplified spontaneous emission (ASE) is realized based on the mixed-Br/Cl perovskite films. By changing the duration of VAE treatment, the ASE peak can be tuned from 537nm down to 475nm. This work not only presents a facile method to prepare high quality mixed halide Cs-based perovskite films, but also pave the way for further exploration of stable blue perovskite lasing.

Influence of Atmospheric Constituents on Spectral Instability and Defect-Mediated Carrier Recombination in Hybrid Perovskite Nanoplatelets

Influence of Atmospheric Constituents on Spectral Instability and Defect-Mediated Carrier Recombination in Hybrid Perovskite Nanoplatelets

Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws

This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or Fisher-KPP type. Under suitable structural assumptions, it is shown that this class of equations underlies two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a Hopf bifurcation around a critical value of the wave speed. The second family pertains to arbitrarily large period waves which arise from a homoclinic bifurcation and tend to a limiting traveling (homoclinic) pulse when their fundamental period tends to infinity. For both families, it is shown that the Floquet (continuous) spectrum of the linearization around the periodic waves intersects the unstable half plane of complex values with positive real part, a property known as spectral instability. For that purpose, in the case of small-amplitude waves it is proved that the spectrum of the linearized operator around the wave can be approximated by that of a constant coefficient operator around the zero solution and determined by a dispersion relation which intersects the unstable complex half plane. In the case of large period waves, we verify that the family satisfies the assumptions of the seminal result by Gardner (Spectral analysis of long wavelength periodic waves and applications, J. Reine Angew. Math. 491 (1997), 149–181) of convergence of periodic spectra in the infinite-period limit to that of the underlying homoclinic wave, which is unstable. A few examples are discussed.

Spectral Instability of Layered Mixed Halide Perovskites Results from Anion Phase Redistribution and Selective Hole Injection.

Despite the ability to precisely tune their bandgap energies, mixed halide perovskites (MHPs) suffer from significant spectral instability, which obstructs their utilization for the rational design of light-emitting diodes. Here, we investigate the origin of the electroluminescence peak shifts in layered MHPs containing bromide and iodide. X-ray diffraction and steady-state absorption measurements prove effective integration of iodide into the cubic lattice and the spatially uniform distribution of halides in the ambient environment. However, the applied electric field during the device operation is found to drive the systematic halide migration. Quantum mechanical density functional theory calculations reveal that the different activation energies required for directional ion hopping lead to the redistribution of anions. In-depth analyses of the electroluminescence spectra indicate that the spectral shifting rate is dependent on the drift velocity of halides. Finally, it is suggested from our study that the dominant red emission is ascribed to the thermodynamically favorable selective hole injection. Our mechanistic study provides insights into the fundamental reason for the spectral instability of devices based on MHPs.

Models of zero-range interaction for the bosonic trimer at unitarity

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered (the unitarity regime). The subject has several precursors in the mathematical literature. We proceed through an operator-theoretic construction of the self-adjoint extensions of the minimal operator obtained by restricting the free Hamiltonian to wave-functions that vanish in the vicinity of the coincidence hyperplanes: all extensions thus model an interaction precisely supported at the spatial configurations where particles come on top of each other. Among them, we select the physically relevant ones, by implementing in the operator construction the presence of the specific short-scale structure suggested by formal physical arguments that are ubiquitous in the physical literature on zero-range methods. This is done by applying at different stages the self-adjoint extension schemes à la Kreĭn–Višik–Birman and à la von Neumann. We produce a class of canonical models for which we also analyze the structure of the negative bound states. Bosonicity and zero range combined together make such canonical models display the typical Thomas and Efimov spectra, i.e. sequence of energy eigenvalues accumulating to both minus infinity and zero. We also discuss a type of regularization that prevents such spectral instability while retaining an effective short-scale pattern. Besides the operator qualification, we also present the associated energy quadratic forms. We structured our analysis so as to clarify certain steps of the operator-theoretic construction that are notoriously subtle for the correct identification of a domain of self-adjointness.

Bound states in semi-Dirac semi-metals

New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations. Physically relevant sufficient and necessary conditions to guarantee the existence of discrete eigenvalues are derived under rather general assumptions on external fields. One of the most interesting features of the analysis is the evident spectral instability of the systems in the weakly coupled regime. The rigorous theoretical results are illustrated by numerical experiments and predictions for physical experiments are made.

High‐Performance Perovskite‐Based Blue Light‐Emitting Diodes with Operational Stability by Using Organic Ammonium Cations as Passivating Agents

AbstractBlue emissive perovskites can be prepared by incorporating chlorine into bromine‐based perovskites to tune their bandgap. However, mixed‐halide perovskites exhibit intrinsic phase instability, particularly under electrical potential, owing to halide migration. To achieve high‐performance blue perovskite‐based light‐emitting diodes (PeLEDs) with operational stability, organic ammonium cations are used for passivating the anionic defects of the CsPbBr2Cl film. Diphenylpropylammonium chloride (DPPACl), used as a passivating agent, successfully prevents the spectral instability of blue PeLEDs by passivating the Cl− vacancies. Consequently, the blue PeLED prepared with this passivating agent delivers excellent device performance with a maximum external quantum efficiency of 3.03%. Moreover, upon tuning the DPPACl concentration, the PeLED emits stably in the deep‐blue spectral region (464 nm) with a half‐life time of 420 s. Thus, the use of organic ammonium cation as a passivating agent is an effective strategy for developing high‐performance blue PeLEDs with operational stability.

Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations

We show that the peaked periodic traveling wave of the reduced Ostrovsky equations with quadratic and cubic nonlinearity is spectrally unstable in the space of square integrable periodic functions with zero mean and the same period. We discover that the spectrum of a linearized operator at the peaked periodic wave completely covers a closed vertical strip of the complex plane. In order to obtain this instability, we prove an abstract result on spectra of operators under compact perturbations. This justifies the truncation of the linearized operator at the peaked periodic wave to its differential part for which the spectrum is then computed explicitly.

Nonlinear spectral instability of steady-state flow of a viscous liquid past a rotating obstacle

We show that a steady-state solution to the system of equations of a Navier–Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $$\mathcal {L}$$ has a part of the spectrum in the half-plane $$\{\lambda \in \mathbb {C}; \mathrm{Re}\, \lambda >0\}$$ . Our result does not follow from known methods, mainly because the basic nonlinear operator is not bounded in the same space in which the instability is studied. As an auxiliary result of independent interest, we also show that the uniform growth bound of the $$C_0$$ -semigroup $$\mathrm {e}^{\mathcal {L}t}$$ is equal to the spectral bound of operator $$\mathcal {L}$$ .

Cavity-Enhanced Photon Emission from a Single Germanium-Vacancy Center in a Diamond Membrane

The nitrogen-vacancy center in diamond has been explored extensively as a light-matter interface for quantum information applications, however it is limited by low coherent photon emission and spectral instability. Here, we present a promising interface based on an alternate defect with superior optical properties (the germanium-vacancy) coupled to a finesse $\approx11{,}000$ fiber cavity, resulting in a $31^{+11}_{-15}$-fold increase in the spectral density of emission. This work sets the stage for cryogenic experiments, where we predict a measurable increase in the spontaneous emission rate.

Intermolecular forces and correlations mediated by a phonon bath.

Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born-Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.

Metal halide perovskites for blue light emitting materials

Metal halide perovskites are considered excellent light emitting materials due to their high photoluminescence quantum yields, tunable spectral wavelength, and outstanding carrier transport properties. By taking advantage of these characteristics, perovskite light-emitting diodes (PeLEDs) can be fabricated via solution processing techniques. PeLEDs, thus, show great promise in display and lighting applications. Accordingly, external quantum efficiencies over 20% have been achieved in green- and red-PeLEDs. However, the performance of blue PeLEDs still lags far behind its red and green analogs. In this review, we summarize the recent progress of blue PeLEDs based on the halogen regulation strategy and the quantum confinement strategy. We discuss the challenges from aspects of poor charge injection, spectral instability, and high defect-states density encountered in blue PeLEDs. We make an outlook on feasible future research directions for highly efficient and stable blue PeLEDs.

Thermodynamic Control in the Synthesis of Quantum-Confined Blue-Emitting CsPbBr3 Perovskite Nanostrips.

Size control is critical in the synthesis of quantum-confined semiconductor nanocrystals, otherwise known as quantum dots. The achievement of size-uniformity and narrow spectral line-width in quantum dots conventionally relies on a very precise kinetic control of the reactions, where reaction time plays a significant role in defining the final crystal sizes and distribution. Here, we show that synthesis of quantum-confined perovskite nanostrips could be achieved through a thermodynamically controlled reaction, using a low-temperature and ligand-rich approach. The nanostrip growth proceeds through an initial one-dimensional (1D) nanorod stage, followed by the lateral widening of the rod to form a two-dimensional (2D) nanostrip. The spectral characteristics of the final product remain unchanged after prolonged reaction, indicating no signs of crystal ripening and confirming the thermodynamic nature of this reaction. The CsPbBr3 perovskite nanostrips were highly uniform and emit at a deep-blue wavelength of 462 nm with a remarkably narrow line-width of 13 nm. This corresponds to color coordinates of (0.136, 0.049) on the CIE 1931 color space, which fulfils the stringent Rec. 2020 standard for next-generation color displays. The well-passivated nanostrips also possess negligible defects and provide a near-unity photoluminescence quantum yield at 94%. Crucially, the achievement of blue emission through a pure-halide perovskite circumvents the problems of spectral instability that are frequently experienced in mixed-halide perovskite systems. The convenience and scalability of our thermodynamic approach, coupled with the excellent optical attributes, would likely enable these quantum-confined perovskite systems to be the preferred method toward color control in trichromatic display applications.

Efficient and stable blue perovskite light emitting diodes based on defect passivation

Solution-processable metal halide perovskites materials have many advantages, such as adjustable band gap, high photoluminescence quantum yield (PLQY), high color purity, high carrier mobility, low temperature solution process, excellent charge transport property and so on. These make them potential application in the display field. In the past few years, the device performance of perovskite light emitting devices (PeLEDs) have been greatly improved by manipulating the perovskite microstructures through various strategies, such as stoichiometry control, dimensional engineering, defect passivation and so on. At present, except for blue PeLEDs, the external quantum efficiencies (EQEs) over 20% have been achieved for green, red, and near-infrared PeLEDs. The low efficiency of blue PeLEDs is retarding their potential applications in full-color display and solid-state lighting. The main reasons in blue PeLEDs are the poor film coverage of blue perovskite materials and the spectral instability during device operation. In order to improve the quality of perovskite film and device performance, the quasi two-dimensional perovskite materials phenylethylammonium cesium lead bromide chloride (PEA&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;CsPbBr&lt;sub&gt;3–&lt;i&gt;y&lt;/i&gt;&lt;/sub&gt;Cl&lt;sub&gt;&lt;i&gt;y&lt;/i&gt;&lt;/sub&gt;) are used as the main perovskite emission material, by partially replacing Br with Cl to enlarge their bandgap to achieve the blue emission. The Lewis base polyethyleneglycol (PEG) is introduced to passivate the surface trapping defects and improve perovskite film coverage. The potassium bromide (KBr) is introduced to reduce perovskite grain size, suppress mobile ion migration and exhibit excellent spectral stability. Dual additives PEG and KBr are incorporated into the quasi-2D blue perovskite for inhibiting the nonradiative losses by passivating the traps in the perovskite films. Eventually, the PEA&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;CsPbBr&lt;sub&gt;3–&lt;i&gt;y&lt;/i&gt;&lt;/sub&gt;Cl&lt;i&gt;&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt; + PEG + KBr based blue PeLEDs with the emission peak of 488 nm are accompanied, which maximum brightness, current efficiency, and external quantum efficiency reached 1049 cd·m&lt;sup&gt;–2&lt;/sup&gt;, of 5.68 cd·A&lt;sup&gt;–1&lt;/sup&gt;, and of 4.6%, respectively, with high color purity (the Commission Internationale de L'Eclairage (CIE) chromaticity coordinates is (0.0747, 0.2570)) and the narrow full width at half maximum (FWHM) of 20 nm. Compare to the devices without additives, the efficiency has increased by nearly 3 times. Furthermore, the devices also show better spectral stability and operation lifetime. This work provides an effective method of blue PeLEDs toward the practical applications.

Existence and stability of discrete solitons in nonlinear Schrödinger lattices with hard potentials

In this paper we study the discrete solitons in nonlinear Schrödinger lattices with hard potentials. We first derive some sufficient conditions for the existence of discrete solitons in the anti-continuum limit. We then establish some spectral stability and instability results for discrete solitons in the anti-continuum limit using the regular perturbation theory. We also develop asymptotic approximations of the eigenvalues of the linearized stability problem.